But the list was just an estimate, Education Department spokeswoman Melissa McGrath said Tuesday, and bidders were cautioned not to use it for detailed cost estimates.

The state issued the WiFi contract to Education Networks of America last month. First-year costs will run $2.11 million, less than the $2.25 million budgeted by the Legislature — but the contract could potentially run 15 years and cost the state $33.3 million.

“The contractor had to take on all the risk, assuming 340 high schools did sign up in the first year, and would have to pay for it … That’s the way the contract is structured.”

The 340 figure is based on the list provided to bidders — although it’s actually a list of not just high schools, but the state’s 333 high schools, junior high schools and middle schools.

The problem with that list, for purposes of this contract, is that it includes middle schools. The contract parameters are clear: Only schools with ninth- through 12th-graders can sign up for the state’s WiFi service. When middle schools are taken out of the equation, about 249 schools are eligible for WiFi.

On Tuesday, McGrath downplayed the discrepancy — and its impact on the bidding process.

“The department provided rough estimates of secondary schools to help guide vendors, but let them know these were just estimates. We used the best data we had available at that time since the state tracks secondary schools and elementary schools. … The department also made it clear that the number of schools would change based on the number of districts that chose to opt in.”